28ebook29 Grammar TheOxfordGuideToEnglishUsage
28ebook29 Grammar TheOxfordGuideToEnglishUsage
28ebook29 Grammar TheOxfordGuideToEnglishUsage
FN
H
y
Ff
Fp
opp
y
H =x +y
sin =
=
hyp H
adj
x
opp y
cos =
=
tan =
=
hyp H
adj x
ANY TRIANGLE TRIG
A
2
a
b
c
=
=
sin A sin B sin C
c = a + b - 2abcos C
2
R=
F x + Fy
resultan t = arctan
g = 32 ft/s2
weight (W) = m g
F y
F x
F
a = net
m
Ff
T1
=W - Fy
M2
1
mv 2
2
PE = 1000 J
KE = 0 J
h = 10 m
1
2
PE = 0 J
KE =100J
t
PEi
2
m vi
KE f
m ghi
PEf
1
2
2
m vf
30
T2=m2g - m2a
m 2g m1g
m1 + m2
T1
Block
m1
W=mg supported by
three cables
T1 = m1g - m1a
T2 = m2a +
Ff = k FN
FN = m2g
a=
F x + Fy = 0
Collision
m ghf
270
m1 g Ff
m1 + m2
T3
After
CIRCULAR MOTION
T
1
f
2 r
T
1
T
Fc m ac
v 1o
v 2o
v 1f
v 2f
v 1o
Collision
v 2o
p = mv J = Ft
2 r
v
v
ac
v2
r r
ac
KE i
180
T2
T1
150
T2
Ep m gh
W Fd
If m2 > m1
T1=m1g + m1a
a=
ENERGY
Ek
90
M1
Ff = FN
Fy = F sin
FN
Fx = F cos
m2
T2
COMPUTING TENSIONS
T = mg - ma
mass
T
moving
downward
m
mass
moving
upward
Fp = mgsin
Ff = FN
TENSIONS
T = mg + ma
W = Weight of Block
FN = Normal Force
Fp = Force parallel to plane
Ff = Force of friction
After
ac
m1 + m2
Ft = mv
4 2 r
T2
Fc
Fc
m v2
r
m 4 2 r
T2
normal
106
105
mega (M)
normal
-----------
104
103
----------kilo (k)
102
101
hecto (h)
deka (da)
n1 sin 1 = n2 sin 2
n2
n
1
r = 90
Refracted
sin c =
milli (m)
-----------
c = critical
'
1
angle
Glas
n2
c/v where v is
2 = the angle of refraction nthe= speedof
light
'
1 = the angle of reflection in the medium.
Law of reflection: 1 = 1'
Law of refraction: n1 sin 1 = n2 sin 2
Snells
n = index of refraction of
the medium
ROTATIONAL MECHANICS
Moment of Inertia
2
1
I sphere mr 2
I cyl mr 2
5
2
mr
rodcg
1
12
m L I rodend
2
Variable
Displacement
ax
Acceleration
ay
vx
Final Velocity
vy
v ix
Initial
Velocity
v iy
Elapsed Time
mL
1
T
f
Translational Equilibrium
F up F down
f fo
v vo
v = speed of sound
v o = vel. of observer
v vs
v s = velocity of source
f o = actual frequency
f = perceived
c w ccw
L I
I 1 1 I 2 2
conservation
b
b
t o the head
b
s
a
b.
KINEMATICS EQUATIONS
x = vix t +
1 2
at
2 x
v y = viy + ay t
1
x = (vix + vx )t
2
v 2x = v 2ix + 2ax x
y=
1
(v + v y )t
2 iy
1
y = viyt + a yt 2 v 2y = v 2iy + 2ay y
2
g = 9.8
m
s2
g = 32
ft
s2
Angular Momentum
Rotational Equilibrium
L mvr
T = 2
Torque
Fd
y Component
v f
Consider
v x = vix + ax t
I hoop m r
s = a + b
KINEMATICS VARIABLES
m
v
Error
x 100%
accepted value
%Error =
n1
Air
hoop
D=
Vector Addition
micro () 10-6
Error = accepted value - experimental value
normal
10-4
10-5
-----------
Reflected
n2
n1
10-2
10-3
centi (c)
K = C + 273
F = 1.8 C + 32
C = F - 32
1.8
C = K - 273
100
10-1
Base Unit
deci (d)
n2 < n 1
MEASUREMENT
n1
n2
n2 > n1
l
g
v=0
U = max
KE = 0
v=0
mgsin mg mgcos
U = max v = max
KE = 0
U = min
KE = max
equilibrium position
Magnetism
2 .Units:
a = [m/sec 2]
F = [kgm/sec 2] (newton)
work = pe= ke = [kgm 2/sec 2] (joule)
3. An ev is an energy unit equal to 1.6 x 10 -19 joules
4. Gravitational potential energy increases as height increases.
5. Kinetic energy changes only if velocity changes.
6. Mechanical energy (pe + ke) does not change for a free
falling mass or a swinging pendulum. (when ignoring air
friction)
7. The units for power are [joules/sec] or the rate of change
of energy.
Wave Phenomena
2. Light slows down, bends toward the normal and has a shorter
wavelength when it enters a higher (n) value medium.
2. Magnetic fields point from the north to the south outside the
magnet and south to north inside the magnet.
4. Blue light has more energy. A shorter wavelength and a higher frequency
than red light (remember- ROYGBIV).
5. The electromagnetic spectrum (radio, infrared, visible.
Ultraviolet x-ray and gamma) are listed lowest energy to highest.
6. A prism produces a rainbow from white light by dispersion (red bends the
least because it slows the least).
7. Light wave are transverse (they can be polarized).
8. The speed of all types of electromagnetic waves is 3.0 x 108 m/sec in a
vacuum.
9. The amplitude of a sound wave determines its energy.
10. Constructive interference occurs when two waves are zero (0) degrees
out of phase or a whole number of wavelengths (360 degrees.) out of
phase.
11. At the critical angle a wave will be refracted to 90 degrees.
Geometric Optics
1. Real images are always inverted.
2. Virtual images are always upright.
3. Diverging lens (concave) produce only small virtual
images.
4. Light rays bend away from the normal as they gain speed
and a longer wavelength by entering a slower (n) medium
{frequency remains constant}.
5. The focal length of a converging lens (convex) is shorter
with a higher (n) value lens or if blue light replaces red.
Modern Physics
1. The particle behavior of light is proven by the photoelectric
effect.
2. A photon is a particle of light {wave packet}.
3. Large objects have very short wavelengths when moving and
thus can not be observed behaving as a wave. (DeBroglie
Waves)
Electricity
Nuclear Physics
1. Alpha particles are the same as helium nuclei and have
the symbol .
2. The atomic number is equal to the number of protons
(2 for alpha)
3. Deuterium is an isotope of hydrogen
4. The number of nucleons is equal to protons + neutrons
(4 for alpha)
Energy
1. Mechanical energy is the sum of the potential and kinetic
energy.
m1
m2
F =
Object Distance (d o )
do is + if the object is in front of the mirror (real object)
do is - if the object is behind the mirror (virtual object)
Image Distance (d i )
di is + if the image is in front of the mirror (real image)
di is - if the image is behind the mirror (virtual image)
Magnification (m)
m is + for an image that is upright with respect to the
object
m is - for an image that is inverted with respect to the
object
SERIES CIRCUIT
UNIVERSAL GRAVITATION
Gm1 m 2
r2
r
This is Newton's Law of Gravity (or more formaly Newton's Law of Universal Gravitation). It was
discovered by Newton in 1665 (327 before 1992) when he was only 23 years old. It states that any two
point masses attract one another with a force that is directly proportional to the product of their masses
and inversely proportional to the square of the distance between them. This equation is exact only for
point masses or sperical masses of uniform density. It's also exact for spherical masses of non-uniform
density if the density of the spherical mass varies as a function of radius only. If the density of the
spherical mass varies as a function of lattitude or longitude (or both) then this equation does not apply
exactly. The constant of proportionality, G, which is called the Universal Gravitational Constant, was
found by experiment to be equal to 6.6732E-11 NT-M2/KG2. The determination of this constant, first done
by the English physicist Henry Cavendish in 1797, is known as "the Cavendish experiment" and is also
called "weighing the Earth".
PARALLEL CAPACITORS
PARALLEL CIRCUIT
R1
R T = R1 + R 2 + R 3
R2
R3
R2
C1
R1
C2
R3
Adding a resistor in series increases the total
resistance of a circuit.
All resistors in series have equal current (I).
it =
V
RT
1
1
1
1
=
+
+
R T R 1 R2 R3
C T = C 1 + C 2 + C 3 + ......
Obser v e r
v +v
fo = fs v vo
- s
C3
vs
vo
CAPACITANCE
-
q1
F
r 2
k = 9 x 109 Nm2/C 2
Unlike : Att rac t
-
Li ke : Repe ll
q
Wire
q
i=
t
Electric current is the flow of charge
through a solid, liquid, gas, or vacuum. It
is the amount of charge passing a certain
cross section divided by the time it takes
to pass. The SI unit of current is the
Ampere. An ampere is the rate of charge
flow equal to one coulomb per second.
OHMS LAW
Vb
RESONANCE
V
I =
R
C
L
V
2a
F
q
TRANSFORMER
Prim a ry
W indi ng
Secon dary
W indi ng
f=
V1 I 1 = V 2 I 2
1 = primary
2 = secondary
N = turns
I = current
V = voltage
I1
N2
=
I2
N1
1
2 LC
r
wire
Lo a d
AC
I ro n
CURRENT
k q1 q 2
16 V
V 1 N1
=
V 2 N2
--- -
F =
E=
q
V
+ +
+ + +
+ ++++
+ +
+
Va
COULOMBS LAW
+
+
+
+
+
+
+
+
C =
B=
0 I
2r
0 = 4 x 10 -7
Tm
A
xF x q
x
x
v
+
SOLENOID B
SERIES CAPACITORS
1
1
1
1
=
+
+
+ .....
CT C1 C2 C3
I
B = 0N I
L
C1
C2
C3
r = mv
qB
F would point to the right for a
negative charge
KEPLERS LAWS
TORQUE
Top
t
Fsi n
Sun
planet
Top
Side
r
Fsi n
a=0
A
x=-A
a=max
T2 =
4 2 a3
GM
focus
a = semimajor axis
i = initial velocity
P E =max
P E= m a x
SIMPLE MACHINES
f
x =0
x=A
Hydraulic Press
f
F
=
a
A
1
PE = k x2
2
SHM-PE
x=-A
v=0
P E= 0
x=A
a =- k x
m
UNITS
radians
radians
=
=
s
s2
t=s
= radians
1 rev = 2 radians
A
x=0
SHM-Acc. (a)
focus
M = mass of Sun
Nm2
G = 6.67 x 10 -11 2
kg
Side
axis
t = r F sin
t
ROTATIONAL KINEMATICS
1
= i + t
= ( i + )t
2
1 2
2
D = it + t
= i2 + 2
2
= Displacement
C
= final velocity
t = time
= acceleration
v = - m a x v=max
v=0
F
A
x = -A
A
x= 0
SHM-Per. (T) T = 2
x=A
m
k
x=-A
SHM-Velocity
v =
A
x= 0
x=A
k
2
2
m (A - x )
f
R
FR =f r
FORCE on a
BRAGG EQUATION
IRRADIANCE
incident r a y
I = P
A
50 W a t t s
reflected rays
5 m2
2d sin
plane o f atoms
10
W/ m 2
50 W a t t s
1 m2
50
CONVEX LENSES
refracted rays
intersection gives
image location on
parallel
object
principal
image
m = - di
do
m = hi
1
1
1
+
=
do
di
f
Converging
Lenses
ho
do is + if the object is in front of the lens
do is - if the object is in back of the lens
di is + if the image is in back of the lens
di is - if the image is in front of the lens
f is + for a converging lens
(sometimes called a convex or positive lens)
f is - for a diverging lens
(sometimes called a concave or negative lens)
Diverging
Lenses
Case#
Object
Position
Image
Position
Image
Type
Size of
Image
Relative to
Object Size
Image
Orientation
Relative to
Object
Infinite
Beyond 2F
At F
Real
Reduced
Inverted
II
Finite
Beyond 2F
Between
F & 2F
Real
Reduced
Inverted
III
At 2F
At 2F
Real
Same size
as object
Inverted
IV
Between
2F & F
Beyond 2F
Real
Enlarged
Inverted
At F
No Image
No Image
No Image
No Image
VI
Between
F & O
Same side
as object
Virtual
Enlarged
Erect
Virtual
Reduced
Erect
All
CONCAVE MIRRORS
Concave
Mirrors
CONVEX MIRRORS
A
O
F
i
C
Convex
Mirrors
W /m 2
Size of
Image
Image
Orientation
Relative to Relative to
Object Size
Object
Case#
Object
Position
Image
Position
Image
Type
Infinite
Beyond C
At F
Real
Reduced to
a point at F
Inverted
II
Finite
Beyond C
Between
C&F
Real
Reduced
Inverted
III
At C
At C
Real
Same size
as object
Inverted
IV
Between
C&F
Beyond C
Real
Enlarged
Inverted
At F
No Image
No Image
No Image
No Image
VI
Between
F&A
Behind
Mirror
Virtual
Enlarged
Erect
All
Anywhere in
Front
Behind
Mirror
Virtual
Reduced
Erect
sphere
I = 2/5 mr2
P1 V1 = P2 V2
I = mr2
sp = 1
sp >1
PRESSURE in a LIQUID
Po
PV = nRT
P = P o +d gh
h
disk
I = 1/2 mr2
Ph
P1V1T 2 =
rod
I = 1/12 ml2
T is in Kelvins
1 = old
2 = new
PROJECTILE MOTION
Ground to Ground
[v sin ]
H= o
vy
2g
vx
tup = tdown
a y = constant
vx is constant
R=
Conservation of Filth:
vo2 sin[2 ]
g
13
10
L = k L T
T1
11
14
15
16
17
A=r 2
C=d
C=2r
12
Sph er e
V = 4 r 3
3
r
V = r 2h
m
s2
cm
1Dyne = 1g 2
s
1N = 1kg
x =
-b
A = 1/2bh
b 2 - 4ac
2a
T2
L
Linear Ex pans io n
18
vy = 0 at max height
2v sin
T= o
g
vy v
o v x = vo cos
v y = vo sin
vx
B = dVg
sp=1
ring
sp < 1
P1 P2
=
T1 T2
ARCHIMEDES PRINCIPLE
(BUOYANT FORCE)
GAS LAWS
ROTATIONAL DYNAMICS
v(avg) = s/t!
!
vf = vi + at!
!
s = 1/2 ( vo + vf) t!
s = vot + 1/2 at2!!
vf2 = vi2 + 2as! !
F = ma!!
!
w = mg!!
!
F = (Gm1m2)/r2! !
p = mv! !
!
J = Ft! !
!
Ft = mv!!
!
T=mg ma!
!
Fk = kFN!
!
Fs = sFN!
!
Fnet = Fapplied- Ffriction!
!
!
!
Energy !
!
!
!
!
W = Fscos! !
P = W/t = Fs/t = Fv!
PE = mgh!
!
KE = 1/2 mv2! !
F = kx! !
!
PEs = 1/2 kx2! !
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Internal Energy ! !
!
!
!
!
Q = mcT!
!
!
Qf = mHf!
!
!
Qv = mHv!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Waves and Optics!
T = 1/f! !
!
v = f
n = c/v! !
!
sinc = 1/n!
!
n1sin1 = n2sin2!
n1v1 = n2v2!
!
/d = x/L!
!
1/do + 1/di = 1/f!!
M = hi/ho = - di/do!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Symbols
a = acceleration
r = dist. between centers
F = force
g = accelertion due to gravity
G = universal gravitation constant
J = impulse
m = mass
p = momentum
s = displacement
t = time
v = velocity
T = tension
w = weight
h = height
Fc = centripetal force
FN = normal force
Fk = force of kinetic friction
Fs = force of static friction
k = coefficient of kinetic friction
s = coefficient of static friction
k = spring constant
PE = potential energy
KE = kinetic energy
P = power
PEs = PE stored in spring
W = work
x = change in spring length
c = specific heat
Hf = heat of fusion
Hv = heat of vaporization
Q = amount of heat
T = change in temperature
F = kq1q2/r2!
E = F/q!!
V = W/q!
E = V/d!!
I = q/t! !
Symbols
D = density
P = pressure F = force
A = cross sectional area
L = change in length
L = original length
Y = Youngs modulus
Ph = hydrostatic pressure
Fb = buoyant force
V = volume
T = temperature
V = change in volume
= coefficient of linear expansion
= coefficient of volume expansion
R = gas constant
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
B = flux density
F = force
k = electrostatic constant
V = electric potential difference
E = electric field!
!
!
V = IR! !
!
P = VI = I2R = V2/R!
W = Pt = VIt = I2Rt!
F = qVB!
!
V = Blv!!
!
F = BIl! !
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
q = charge
Series Circuits!
!
!
!
!
It = I1 = I2 = I3 =.....!
!
Vt = V1 + V2 + V3 +..! !
Rt = R1 + R2 + R3 + ..!!
!
!
!
!
v = velocity
l - length of conductor
I = current!
!
R = resistance
V = electric potential difference
Parallel Circuits
It = I1 + I2 + I3 +.....
Vt = V1 = V2 = V3 = ....
1/Rt = 1/R1 + 1/R2 + 1/R3 + ....
Transformers!
!
!
Np/Ns = Vp/Vs!
VpIp = VsIs!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Modern Physics! !
Wo = hfo!
!
Ephoton = hf!
!
KEmax = hf - Wo!!
p = h/
Ephoton = Ei - Ef! !
!
!
!
!
!
!
!
!
!
!
!
!
T1/2 = 0.693/
N = Noe-t!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Wo = work function
c = speed of light in vacuum
f = frequency
fo = threshold frequency
h = Plancks constant
p = momentum
= wavelength
KE = kinetic energy
!
!
!
!
!
!
m = mass
E = energy
Nuclear Energy ! !
!
!
E = mc2!
!
!
!
!
!
!
!
!
!
!
!
!
Circular/Periodic Motion!
!
!
!
!
ac = v2/r!
!
!
Fc = mv2/r!
!
!
v = 2r/T!
!
!
T = 2 (l/g)1/2 [pendulum]!
g = GM/d2!
!
!
vescape=[2GME/re]1/2! !
Tsatellite = 2[(r3/GME)]1/2!
!
!
!
!
!
!
!
r = radius
Fc = centripetal force
v = velocity
ac = centripetal acceleration!
T = period
ME = mass of Earth
rE = radius of earth
Symbol!
Avogadros number!
!
Electron Charge!
!
Plancks Constant!
!
Mass of electron!
!
Mass of neutron!
!
Mass of proton! !
!
Speed of light (vacuum)!
Universal Gravitational! !
Universal Gas Constant!
Electrostatic Constant! !
NA!
e!
h!
me!
mn!
mp!
c!
G!
R!
k!
Value
!
!
!
!
!
!
!
!
!
!
6.02 x 1023
1.6 x 10-19
6.63 x 10-34 J s
9.1 x 10-31 kg
1.67 x 10-27 kg
1.67 x 10-27 kg
3 x 108 m/s
6.67 x 10-11 N m2/kg2
8.314 J/mol K
9.0 x 109 N m2/C2
1 in = 2.54 cm! !
!
1 ft = 0.3048 m!!
!
1 mi = 5280 ft = 1.609 km!
1 m = 3.281 ft! !
!
1 km = 0.6214 mi!
!
1 angstrom = 1 x 10-10 m
!
!
!
!
!
Mass!!
Power
Time! !
Pressure
Speed!
Volume
1 lb = 4.448 N! !
!
1 N = 105 dynes = 0.2248 lb!
Angle
!
!
1 radian = 57.30
1 = 0.01745 radian
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Symbol!
T!
!
G!
!
M!
!
k!
!
h!
!
da!
!
d!
!
c!
!
m!
!
!
!
n!
!
p!
!
10
!
!
!
!
!
!
!
!
!
!
!
!
Mass! !
!
Radius (eq)!
!
Earth-Sun Dist! !
!
!
!
5.98 x 1024 kg
6.38 x 106 m
1.50 x 1011 m
Mass! !
!
Radius!!
!
Earth-Moon Dist!
!
!
!
7.35 x 1022 kg
1.74 x 106 m
3.85 x 108 m
Mass! !
Radius!!
!
!
1.99 x 1030 kg
6.96 x 108 m
Earth Gravity! !
!
Atm. Pres (sea level)! !
Density of air (STP)!
!
Speed of sound in air (20C)!
Water
!
!
!
!
Earth
!
!
!
Moon
!
!
!
Sun
!
!
Density (4C)!
Hf!
!
Hv!
!
c!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Factor
1012
109
106
103
102
101
10-1
10-2
10-3
10-6
10-9
10-12!
!
!
Vectors Components
Vectorx = (Vector) cos !
Vectory = (Vector) sin
SI Base Units
Quantity!
Force!!
Unit! !
length! !
meter! !
mass! !
kilogram!
time! !
second!!
amount of
substance!
mole! !
temperature! kelvin! !
electric current! ampere!!
luminous
intensity!
candela!
Vector Resolution
y
Abbr.! !
Apparatus
m!
kg!
s!
!
!
!
ruler
balance
stopwatch
mol!
K!
A!
!
!
!
............
thermometer
ammeter
cd!
light meter
x
Ax = A cos
Ay = A sin
A2 + B2 = C2
sin = A/C
C
A
cos B/C
tan = A/B